Question

1200 soldiers in a fort had enough food for 28 days. After four days some soldiers were transferred to another fort and thus the food lasted for an extra 32 days.How many soldiers left the fort?

Answer 1

Answer:

300

Step-by-step explanation:

Total amount of food available initially:  1200 * 28    Soldier-days

After 4 days, the amount of food remaining:  1, 200 * 24  soldier-days worth.

Let N soldiers be remaining after some are transferred to another fort.

    1, 200 * 24  = N * 32

              N = 900

 Hence,  300 soldiers were transferred.

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Proportional method

    As the number of soldiers decreases, the number of days the food lasts will increases.  As the number of soldiers increases, the number of days the food lasts, will decrease.  So number N  of soldiers is inversely proportional to the number D of days.

              So    N = K / D,    where  K = constant of proportionality

                    when  N = 1,200  then  D = 24

            So  K = N D = 1,200 * 24

 

      When D = 32,  N = K / D = 1, 200 * 24 / 32 = 900

    Hence, there were only 900 soldier after 4 days.    So 1200 - 900 = 300 soldiers are transferred.